A Mean-Reverting Jump Diffusion Process

​
initial value
4
jump intensity
6
volatility of continuous component
0.8
reversion parameter
1
mean jump size
0
standard deviation of jump size
1
duration
1
vertical range
10
randomize
This Demonstration shows a path of a mean-reverting jump diffusion process (with mean 0) with normally distributed jumps. Such processes can be used for modelling the logarithm of the price of a commodity such as gas, oil, etc. that is subject to irregular disruptions but tends to revert to the mean (the production cost of the commodity).

Details

The stochastic process modelled here is described by the stochastic PDE:
d
Z
t
=-α
Z
t
dt+σd
W
t
+
J
t
d
N
t
,
where
W
t
is the standard Wiener process,
J
t
is normally distributed, and
N
t
is a Poisson process. The coefficient
σ
is the volatility of the continuous random component of the process and the coefficient
α
is the rate of mean reversion. In order to obtain rapid return to the mean after "spikes" that one observes in electric energy markets,
α
has to be set to a high value.

References

[1] T. Kluge, "Pricing Swing Options and other Electricity Derivatives"[doctoral thesis], Oxford, 2006.

External Links

Merton's Jump Diffusion Model
Mean-Reverting Random Walks

Permanent Citation

Andrzej Kozlowski
​
​"A Mean-Reverting Jump Diffusion Process"​
​http://demonstrations.wolfram.com/AMeanRevertingJumpDiffusionProcess/​
​Wolfram Demonstrations Project​
​Published: June 11, 2012